Answer:
Step-by-step explanation:
Confidence interval is written in the form,
(Sample mean - margin of error, sample mean + margin of error)
The sample mean, x is the point estimate for the population mean.
Margin of error = z × s/√n
Where
s = sample standard deviation = 0.67
n = number of samples = 103
From the information given, the population standard deviation is unknown hence, we would use the t distribution to find the z score
In order to use the t distribution, we would determine the degree of freedom, df for the sample.
df = n - 1 = 103 - 1 = 102
Since confidence level = 99% = 0.99, α = 1 - CL = 1 – 0.99 = 0.01
α/2 = 0.01/2 = 0.005
the area to the right of z0.005 is 0.005 and the area to the left of z0.005 is 1 - 0.005 = 0.995
Looking at the t distribution table,
z = 2.6249
Margin of error = 2.6249 × 0.67/√103
= 0.173
Confidence interval = 98.6 ± 0.173
This suggests that the mean body temperature could very possibly be
98.6degrees°F.
